1. Field of the Invention
This invention relates to the design and analysis of water distribution systems and particularly, to variable speed pumps used in such designs.
2. Background Information
In many civil engineering applications, and in particular, in water distribution networks for cities, townships and municipalities, it is of the utmost importance to design such systems accurately and to predict water pipe flow and hydraulic pressure conditions for the water network in any particular area. This is to design, build, maintain, and operate water infrastructure efficiently and to ensure the availability of the potable water resource to the community.
Water distribution systems are often described using software for this purpose. A hydraulic network solver (often commonly referred to as a “solver”) is a computer program that simulates and predicts water pipe flow and hydraulic pressure conditions for the links (such as pipes) and the nodes (such as junctions) in such a system. This information is useful and important when designing a new system (for a new subdevelopment) or when designing additional components such as pumps, valves and water storage devices that are to replace aging components or for performing other rehabilitative measures, and to evaluate efficient operating strategies.
One hydraulic network solver that is in use today is the EPANET Solver. This is public domain software that has been adopted for use in the industry and which is made freely available by the U.S. Environmental Protection Agency, of Washington D.C. The EPANET solver uses mathematical matrices to describe the hydraulic system. When solving such matrices for system heads and flows, the EPANET Solver utilizes the Cholesky factorization technique and is highly optimized for the solution of the symmetric matrix that describes the problem.
In general, many factors affect the mathematical representation of a hydraulic network, and in particular, the water pipe flow and hydraulic pressure conditions at any particular point in a network. For example, there are junctions in the network where flow is affected. A valve in a water storage tank or a reservoir may be on or off. Routine day-to-day demand is also an important factor to be taken into consideration when mathematically describing a water distribution system, or portion of such a system.
Fixed speed pumps differ from variable speed pumps in that they operate at a known and constant speed. Since demand can vary throughout the day or other time periods, variable speed pumps adjust their speed in compensation and in so doing adjust flow, improve pressure maintenance, and reduce energy usage. However, it has been difficult for the characteristics of such variable speed pumps to be taken into account appropriately in hydraulic network solvers because of the non-symmetric aspects, which are thus introduced into the matrices providing solutions for a system that includes variable speed pumps.
The mathematical term often used to describe a variable speed pump in a system is a relative speed factor. Existing state of the art hydraulic solvers include the relative speed factor in the calculation of head and flow, but those solvers do not typically calculate or estimate a relative speed factor for a variable pump speed in the system. Instead, they require the user to input the relative speed factor describing the operation of a pump, in the first instance. However, under many circumstances, it would be helpful for a user to be able to determine an optimal relative speed factor for a particular point in the network needed to meet a predetermined operating objective (such as maintaining a constant head). Up to now, this was accomplished using a trial and error process. More specifically, an engineer typically chose a relative speed factor, entered that into the appropriate equation, and then ran the hydraulic network solver to check whether the operating objective has been met. If it was not met to sufficient tolerances, a different relative speed factor was then entered and the program was rerun. This process was repeated until the operating condition had been met. This can be extremely time consuming and tedious. This process is further complicated when practical applications of variable speed pumps are also considered. For example, factors that can affect variable speed pumps and relative speed estimation, include pump scheduling, manual control override, emergency shutdowns and other complex control behaviors.
It has been known to provide variable pump speed features in hydraulic network solvers, but known calculations generally treat the relative speed factor as a user-defined parameter, not a parameter that is calculated or estimated as part of a simulation. Alternatively, in some cases, the variable speed pump relative speed factor is developed by software applications that rely on numerical matrix inversion procedures for sparse non-symmetric matrices such as LU factorization. This, however, can lead to complex, non-symmetric equations which involve cumbersome solutions to those equations and which could also in turn involve use of a large memory capacity in the associated computer.
Furthermore, the EPANET Solver, an accepted basic hydraulic solver software, it does not at present include the ability to make a direct parameter estimation with respect to variable pump speeds, nor does it include control modeling capability that allows the user to model and design pumps with variable speed drives. If the EPANET Solver software application program were to be modified to include this feature, based upon its use of the Cholesky factorization method, this modification would be extremely invasive to the programming with large portions of code needing to be rewritten. This would not only be costly and time consuming, but may even lead to unexpected, or even unreliable, results.
There remains a need, therefore, for a software design which allows the user to model and design water networks with variable speed pumps more effectively and efficiently and which further allows such calculations to be made without the dedication of a large portion of memory storage to such estimations.
There remains a further need to provide an extension to the EPANET Solver program to readily allow variable speed pump parameter estimation.
It is an object of the invention to simplify the calculations needed to estimate variable pump speed relative speed factors and to efficiently and reliably solve the system of non-symmetric equations that describe the problem.